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In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…
Clustering is one of the most widely used procedures in the analysis of microarray data, for example with the goal of discovering cancer subtypes based on observed heterogeneity of genetic marks between different tissues. It is well-known…
Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…
When solving partial differential equations (PDEs) using finite difference or finite element methods, efficient solvers are required for handling large sparse linear systems. In this paper, a recursive sparse LU decomposition for matrices…
We propose and analyze a second-order Strang splitting method for a class of stiff matrix differential equations with Sylvester-type structure. The method splits the dynamics into a stiff linear part, treated exactly via matrix…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
There is a rich literature on clustering functional data with applications to time-series modeling, trajectory data, and even spatio-temporal applications. However, existing methods routinely perform global clustering that enforces…
The Paterson--Stockmeyer method is an evaluation scheme for matrix polynomials with scalar coefficients that arise in many state-of-the-art algorithms based on polynomial or rational approximation, for example, those for computing…
A majorized accelerated block coordinate descent (mABCD) method in Hilbert space is analyzed to solve a sparse PDE-constrained optimization problem via its dual. The finite element approximation method is investigated. The attractive…
Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A…
We discuss the electromagnetic scattering and radiation problems of multilayered spheres, reviewing the history of the Lorentz-Mie theory and the numerical stability issues encountered in handling multilayered spheres. By combining…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
Sparse polynomial interpolation, sparse linear system solving or modular rational reconstruction are fundamental problems in Computer Algebra. They come down to computing linear recurrence relations of a sequence with the Berlekamp-Massey…
The enumeration of finite models is very important to the working discrete mathematician (algebra, graph theory, etc) and hence the search for effective methods to do this task is a critical goal in discrete computational mathematics.…
We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous…
In two earlier papers, we designed a distributed deterministic asynchronous algorithm for minimizing the sum of subdifferentiable and proximable functions and a regularizing quadratic on time-varying graphs based on Dykstra's algorithm, or…
In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…
Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…
Boolean quadratic optimization problems occur in a number of applications. Their mixed integer-continuous nature is challenging, since it is inherently NP-hard. For this motivation, semidefinite programming relaxations (SDR's) are proposed…
A new runtime environment for the execution of recursive matrix algorithms on a supercomputer with distributed memory is proposed. It is designed both for dense and sparse matrices. The environment ensures decentralized control of the…